That is not what that verse is saying. Let's look at the context. I'll quote from the NASB since it looks like that is the translation you quoted.
John 6:25 And when they found Him on the other side of the sea, they said to Him, “Rabbi, when did You get here?” 26 Jesus answered them and said, “Truly, truly, I say to you, you seek Me, not because you saw signs, but because you ate some of the loaves and were filled. 27 Do not work for the food that perishes, but for the food that lasts for eternal life, which the Son of Man will give you, for on Him the Father, God, has set His seal.” 28 Therefore they said to Him, “What are we to do, so that we may accomplish the works of God?” 29 Jesus answered and said to them, “This is the work of God, that you believe in Him whom He has sent.
Notice in verse 27 that Jesus told the crowd gathered at Capernaum to "not work for the food that perishes, but for the food that lasts for eternal life". He was speaking figuratively, but He was clearly saying that there was something they had to do in order to obtain eternal life. Then they asked Him what they had to do that God required of them. Jesus answered that what they needed to do was "believe in Him whom He has sent".
Jesus was not saying that them believing in Him was God's doing. You can see that by looking at the context. When He said "this is the work of God" He meant that this is what God requires you to do (the action He required from them) which was to "believe in Him whom He has sent".
It is all of it, "all of it", only under the umbrella if "only if the Father God has willed it", or "has already willed" (or predestinated) "it" only always...
Otherwise your saying there are other things or other wills that are stronger than His (God's) and that are outside of His (God's) power and/or control, and/or ability to reign in or control, etc...
Not to mention, as has already been mentioned a lot already, over and over again, etc, not to mention that, we are also, in some small way or ways, our own saviors to a lesser or greater degree or another if it is in any way based on "us", etc, or what we do or don't do, or choose or don't choose, etc, which makes our wills stronger than God's, and is also "also" a "grace and/or faith plus works" mixture also, etc...
Everything Jesus and/or the apostles said and or told us to choose or not choose, or else do or not do, etc, (choose, etc), was always, "always" always only under the guise or umbrella always of only if God the Father has already chosen it to be or not be or ever already be or become so at all ever, etc, "at all" "ever", etc, and we would all do very, very well to not ever forget that, etc...
Cause to forget that is greatly dishonoring God the Father, etc, cause it is limiting Him, or that One, in a way that He should not ever be considered "limited" at all ever, etc...
God Bless!